UC Santa Barbara

Frequency conversion mechanisms are essential elements in frequency synthesizers, which are used in many applications ranging from microwave and RF transceivers to wireless applications to vibration energy harvesters. In particular, the frequency divider, which is an integral part of the phase-locked loop circuit, is essential in modern day instrumentation and wireless communications. In most systems requiring frequency conversion, electronic frequency converters are used; these components require significant power input and introduce noise into the system. In this dissertation, we introduce a mechanism for eliminating these noisy electronic components by using coupled mechanical elements. This novel mechanism for frequency division using parametric resonance in MEMS relies on finite deformation kinematics and nonlinear coupling between isolated modes in a structure to divide an input signal through multiple stages using purely mechanical coupling.

We present the theoretical framework for a generic subharmonic resonance cascade. Design considerations for one specific implementation are discussed, and a proof-of-concept for low-noise low-power applications is demonstrated. A single input signal is divided through three modal stages, generating output signals at 1/2, 1/4, and 1/8 of the input signal. Coupling and boundary conditions are explored, as well as the noise characteristics of this mechanical frequency divider. We show that this type of cascading frequency conversion improves phase noise performance of each individual mode.